Geometric invariance of mass-like asymptotic invariants

We study coordinate-invariance of some asymptotic invariants, such as the Arnowitt-Deser-Misner mass or the Chruściel–Herzlich momentum, given by an integral over a “boundary at infinity.” When changing the coordinates at infinity, some terms in the change of integrand do not decay fast enough to ha...

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Bibliographic Details
Published in:Journal of mathematical physics 2011-05, Vol.52 (5), p.052504-052504-14
Main Author: Michel, B.
Format: Article
Language:English
Subjects:
Asymptotic methods
Exact sciences and technology
Geometry
Integrals
Mathematical methods in physics
Mathematics
Physics
Sciences and techniques of general use
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Summary:We study coordinate-invariance of some asymptotic invariants, such as the Arnowitt-Deser-Misner mass or the Chruściel–Herzlich momentum, given by an integral over a “boundary at infinity.” When changing the coordinates at infinity, some terms in the change of integrand do not decay fast enough to have a vanishing integral at infinity; but they may be gathered in a divergence, thus having vanishing integral over any closed hypersurface. This fact could only be checked after direct calculation (and was called a “curious cancellation”). We give a conceptual explanation thereof.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.3579137